Problem: What do the following two equations represent? $x+y = 3$ $-x+y = -5$
Solution: Putting the first equation in $y = mx + b$ form gives: $x+y = 3$ $y = -x+3$ Putting the second equation in $y = mx + b$ form gives: $-x+y = -5$ $y = x-5$ The slopes are negative inverses of each other, so the lines are perpendicular.